Potential Definition and 1000 Threads

V at surface = k Q / r = 9 x 109 x (1 x 109 x (-1.6 x 10-19) / (1 x 10-2) = - 144 V V at a point far away = 0 V From the sentence "electric potential difference between the surface of this sphere and a point far away" means that the question asks about V at surface minus V at far away so the...

Hi! hope you are doing well , I'm trying to solve this problem ( mechanical problem) about structure with load F as it showing in the next figure , i want to determine to critical force F , the stability force ( which means if my load is bigger than the critical load my system will be unstable)...

I'm running some molecular dynamic simulations and I came across this, https://en.wikipedia.org/wiki/Star_formation#Cloud_collapse , and I was wondering if there was a specific force potential to use in this case. Supposing I have a ensemble of heated atoms moving around and I cool them down...

a) I take "a point where it is neutral" as the electric potential at that point is zero. Is this correct? And because the two charges are both negative, there can not be any point where V = 0? Am I wrong or maybe one of the charge should be positive? Thanks

I used to believe that potential energy of a particular particle is of no meaning. It is always linked with a system, and Potential Energy of a system means negative of work done by INTERNAL conservative forces from an initial stage of assumed zero potential energy. And energy cannot be said to...

I found the potential at A, however I tried doing it with B but it says I have the wrong answer.

While studying Special Theory of Relativity I came across the formula for the energy of a particle. The total energy of a relativistic particle in STR contains the Rest Mass energy and the Kinetic energy. But, in Classical and Quantum Mechanics, we consider the total energy of the particle to be...

Hi there I have been attempting the parts to this question and I'm finding some trouble on how to answer the last part which is d)iii Here is what I have done for the rest of the parts and what I think I should start off with in part d)iii Thanks!

A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round...

Hello, I start by applying the integral for the vector potential ##\vec{A}## using cylindrical coordinates. I define ##r## as the distance to the ##z##-axis. This gives me the following integral,$$\vec{A} = \frac{\mu_0}{4\pi} \sigma_0 v 2 \pi \hat{x} \int_0^{\sqrt{(ct)^2-z^2}}...

I'm self studying so I just want to ensure my answers are correct so I know I truly understand the material as it's easy to trick yourself in thinking you do! A particle of mass m is in a 1-D infinite potential well of width a given by the potential: V= 0 for 0##\leq## x ##\leq## a =...

I think its going to be intg(dr2)intg(exp(r^2) dr) or something like that.

Many, many years ago while in engineering graduate school I was studying calculus of variations. One classic problem was to determine the shape of a hanging cable supported at its two ends. After minimizing the integral, the catenary curve was the solution. The basic assumption in setting up...

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Based on the conditions, I found that $$V(x)=\frac{a^2}{\pi^2} ρ_0sin(πx/a)$$ would be a solution to Laplace's equation for $$|x|\leq a$$ and $$V(x)=cx+d$$, where c and d are constants. From the boundary conditions, $$\frac{dV(a)}{dx}=\frac{a}{\pi} ρ_0cos(πa/a)=ac$$, $$c=\frac{a\rho}{\pi}$$ and...

I have read that the potential V = E*d for a constant electric field E, so this is related to the battery voltage of some voltage say 12v etc. Because battery will produce voltage using chemical reaction. Above two are different concepts or related? Please advise.

Assume that an infinite metallic plate A lies in the xy-plane, and another infinite metallic plate B is parallel to A and at height z = h. The potential of plate A is 0, and the potential of plate B is constant and equal to V. So, there is a uniform electrostatic field E between plates A and B...

I know that you can get the answer through using Fs as 18 and solving for K, then subbing it into the equation for elastic energy. I was just wondering why another method wouldn't work. I tried doing it using the concept that Work is an equal to the Change in Elastic Energy, therefore Ee=xF...

How to find potential energy if force depends on both position of particle and time ? Suppose force is : f(r,t) = (k/r^2) * exp(-alpha*t), k, alpha = positive constants, r = position of the particle from force-centre t = time Is this force a conservative or non-conservative ?

The final result will only differ in its sign, but this is crucial. Having a positively, radially oriented electric field ##\textbf{E}##, I understand that the sign of the integral should be positive (## - (- A) = A##), but it is not! How and why is this the case? A line integral where the...

Given here is that by geometry r1^2 =r^2 +a^2 - 2ar*cos(theta) But if we try to do vector addition then since direction of dipole is upwards then it should be r^2 =r1^2 +a^2 + 2ar1*cos(alpha) Where alpha is the angle between a and r1. I Don,'t understand how they get it by geometry

If for example I have two charged particles q_1 , q_2 with distance 'r' between them, then: The potential energy that results from particle q_1 exerting force on particle q_2 is $$ k\frac{q_1 q_2}{r} $$ If I do the same process for particle q_2: The potential energy that results...

Summary:: What if you were calculating the voltage potential for a dipole, but underwater? I'm making a predictive model (in R programming) for the voltage potential at any point around a dipole. I need to be able to change parameters, one being the k constant. V=( kpcosѲ)/(r^2). Where V is...

Summary:: if Plate A had a potential of 9V, This means as We approach a unit charge from +Infinity to A we have to do this precise amount of work Now we remove plate A, And replace it with plate B that has a potential of -9V Again that means to go from +Infinity To B we actually gain energy, or...

This is the V(x) diagrams and what I am thinking (really not sure though) is that for the first one you the energy has to reach V2 before it can start transmitting and the graph can take off from T=0, since there is an increase in energy potential that is V2. And as the energy increases, the...

I am having problem with part (b) finding the vector potential. More specifically when writing out the volume integral, $$A = \frac{\mu_0}{4\pi r}\frac{dq}{dt}\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{?}\frac{1}{4\pi r'^2} r'^2sin\theta dr'd\theta d\phi$$ How do I integrate ##r'##? The solution...

Hello, I'm confusing about the basic terms about Conservation of Energy, Potential Energy and Work. Consider that we have a mass ##M## above the ground (zero point) distance of ##y_{0}=h##. When we release the mass it will accelerate through it's way to ground. So the work is made by a field...

Hello, I have a problem where I'm supposed to calculate the charge distribution ρ. I need to calculate it by applying the Laplacian operator to the potential Θ. The potential is the function: q*exp(-αr)/r I found on the internet that for this type of potentials I cannot just apply the...

I am working out an example problem from one of my textbooks and I am a bit confused on why a value is negative. The problem asks: Calculate the final speed of a free electron accelerated from rest through a potential difference of 100 V. This is a conservation of energy problem. Ultimately you...

Imagine a container of salt water at 0V (Relative to ground),Now you've put in it 2 electrodes,one at +500V (Electrode A), The other at +250V(Electrode b), Normally positive ions should go to the negative electrode , and Negative ions should go to the positive electrode , But in our example the...

I get $$B_2(T)=2\pi N\int_{0}^{\infty} (1-e^{-\beta E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)})r^2dr$$ as the coefficient. I was just unsure how to evaluate it numerically from here. Any suggestions would be appreciated. Thank you.

Not even sure where to start.

and when are they the same thing? In quite simple terms.Many thanks

So this is the problem: My only point of confusion right now is in what the value of a is... I'm having trouble finding it anywhere, and online stuff about the yukawa potential just states that it's a parameter. Thanks for any help! Edit: It might be worth noting that gamma equals kq1q2.

I have one-dimensional problem with a one-dimensional potential I want to know the energy domains that will result in discrete energy levels and the energy domains that will result in continuous energy levels In my lecture, my professor gave the example of v(r) = 1/r (r>0) (hydrogen atom...

I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##. After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation...

I am quite familiar with the Ergun equation's formulation. My question is, do I need to subtract the potential term ΔP/Δz = -ρg/gc after the Ergun equation's own ΔP/Δz , assuming that the fluid is to be pumped upward, from the bottom of the bed to the top of the bed? I was thinking it should be...

Firstly, I am not a English speaker. So I apologize that I cannot use English well.. I got a), c), e) a) at 0.5cm, E = -q/(2e_0*A) - Q/(2e_0*A) + q/(2e_0*A) = -1.4*10^7 V/m c) at 1.5 cm, E = 0 (inside electrode) e) at 2.5cm, E = -q/(2e_0*A) + Q/(2e_0*A) + q/(2e_0*A) = 1.4*10^7 V/m And I am...

For the first part, I considered the Force acting on it by all charges as given by $$\vec {F} = \Sigma_{j} \frac{m_{i} m_{j}}{\left(r_j - r_i \right)^{1.5}} \vec{r_j} - \vec {r_i} = \Sigma_j m_i \vec {g_j} $$ Where ##\vec{g_{j}}## represents gravitational acceleration of ##m_i## due to jth mass...

My solutions: When ball is launched horizontally, assuming its velocity is entirely in the horizontal dimension, there is no interaction of the ball with the gravitational field, thus no change in GPE, so all of the EPE (elastic potential energy ) of the spring is transferred to KE of the ball...

Hello, I'm trying to obtain a polarization curve for a fuel cell (two electrodes in HCl). From what I've seen in literatures, current is applied and the voltage is measured. Is it still the same to change the voltage and measure the current instead? For some reason our equipment only have the...

I have one problem with this question that I've been struggling with. Initially, the total energy should be given by E =m1* v0^2/2 (as U goes to zero, and m2 is at rest). However, if we write r = r1 - r2, we get E = mu*rdot^2/2 + U_eff(r), U_eff(r) also goes to 0, where mu is the reduced mass...

This is a problem from a textbook, and I can't solve it. I know that the equation of Potential energy of electric dipole. Since the configuration is a little bit complicated. I'm confused applying which electric fields.

Hello and thanks in advance for your help. For about a week now, I've been trying to write what should be a simple python program. The idea is first to write a program for a simple harmonic pendulum, then adapt it to a spring pendulum. However, in order to do this, I have to write the simple...

I'm not really sure what I need to find exactly. From what I'm seeing, I could give C1 the max potential difference of 125V because it has the lowest capacitance, and because V = Q/C, this means the capacitor with the highest potential difference across its plates will be the one with the lowest...

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In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current...

Hello to everyone. The question or debate here is how you obtain the commonly known equation of dipole electric moment: from the electrostatic potential equation for a multipole of order n: I understand it is related with Dirac delta functions but a step by step solution might be helpful.Thank...

Hi everyone, I recently finished applying to a university for grad school. Previously, I had contacted a professor with whom I wanted to work with, and it seemed they were also interested in taking me as a PhD student. Ideally, would one follow up (by email) with the professor once they've...